Solve for $x$ and $y$ using elimination. ${-3x+6y = 42}$ ${3x+5y = 68}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. $11y = 110$ $\dfrac{11y}{{11}} = \dfrac{110}{{11}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-3x+6y = 42}\thinspace$ to find $x$ ${-3x + 6}{(10)}{= 42}$ $-3x+60 = 42$ $-3x+60{-60} = 42{-60}$ $-3x = -18$ $\dfrac{-3x}{{-3}} = \dfrac{-18}{{-3}}$ ${x = 6}$ You can also plug ${y = 10}$ into $\thinspace {3x+5y = 68}\thinspace$ and get the same answer for $x$ : ${3x + 5}{(10)}{= 68}$ ${x = 6}$